Thanks - but there's a wrinkle. It's vibrating every 2 seconds. If I hold the Power + Volume Down, the phone will shut off eventually and stop vibrating, but if I keep holding it (or press the combo again), I release power after the first vibrate but the phone just starts vibrating again. I've held the combo for 60 seconds, I've held it for 20. I just can't get to the exclamation mark. I've done a few hard resets in the past. So I was hoping WDRT would fix this mess but it doesn't recognize the phone. Tried pulling the battery, tried holding the combo, even tried plugging it into my Surface without a battery (phone actually displayed a missing battery, so at least the screen works)... Maybe I need to leave the phone without its battery for a while...
Regarding the power ...
I made a rookie mistake. I'm in the UK on business and there are switches on the wall for the power sockets. I had my phone plugged in but the switch wasn't turned on so no power. In the US, it's much easier to electrocute yourself. Ugh. What a mess.